(CNN) - Wisconsin's Senate GOP battle is shaping up to end in a close finish Tuesday as voters cast their ballots for the competitive four-way race.

Heading into the contest, a recent poll shows former Wisconsin Gov. Tommy Thompson as the frontrunner in the crowded field of candidates, with businessman Eric Hovde, former Rep. Mark Neumann and state assembly speaker Jeff Fitzgerald following behind.- Follow the Ticker on Twitter: @PoliticalTicker

While Thompson, who made a short-lived presidential bid in 2008, has been at the top of the polls throughout much of the race, his margin over opponents has been dwindling in recent weeks, making the battle even more competitive.

According to a recent Marquette University Law School poll, 28% of likely GOP primary voters back Thompson, while 20% support businessman Hovde. Meanwhile, Neumann has 18% support and Fitzgerald comes in behind with 13%. A significant amount of voters, 21%, remain undecided.

Two other recent polls, however, show Thompson and Hovde in a statistical dead heat.

"The GOP primary race continues to get closer," Marquette Law School Poll Director Charles Franklin said in a statement. "Thompson held a lead of 20 percentage points over Hovde in June, 12 points in July and now 8 points in August. Likewise, Mark Neumann and Jeff Fitzgerald have rebounded from lower levels of support in early July."

The winner of the race will go on to run against Democratic Rep. Tammy Baldwin in the general election. The victor in that race will replace Sen. Herb Kohl, a four-term Democrat who announced he was not running for re-election in May 2011.

While Thompson has high name recognition, he has been out-raised by more than 2 to 1 by Hovde, who currently serves as the CEO of the real estate company Hovde Properties. According to Federal Election Commission filings, Hovde brought in $5.5 million this cycle, compared to Thompson at $2.4 million.

Facing questions about his age, 70-year-old Thompson made headlines last week when he dropped and did 50 push-ups for the editorial board at the Milwaukee Journal Sentinel.

"I do 100 sit-ups in the morning," he told the newspaper. "I do my push-ups and then I do my sit-ups."

Neumann, meanwhile, has seen strong grassroots conservative support. Last week the Tea Party Express endorsed the former congressman, saying he is the "only one with a plan that cuts spending, balances the budget and repeals ObamaCare." Two major conservative super PACs–Senate Conservative Fund and Club for Growth–also back Neumann.

However, another group supportive of tea party-aligned candidates, FreedomWorks, split with other national conservative groups and endorsed Hovde last month.

The fourth candidate, assembly speaker Fitzgerald, is best known for being a chief advocate in the push for Gov. Scott Walker's plan to curb collective bargaining rights for state workers, a law that was praised by national Republicans but ultimately landed the governor in mammoth fight to keep his seat in a high-profile recall effort.

Of the crop of Senate hopefuls, however, Fitzgerald lags far behind in fundraising, bringing in $160,000 this cycle.

Wisconsin also marks an important state in the presidential election. While CNN's electoral map rates the state as leaning towards Obama in the fall election, Mitt Romney's selection of Rep. Paul Ryan as his running mate this weekend suggests that the Romney campaign considers the Badger State up for grabs in November.

In June, shortly after Gov. Walker survived the contentious recall effort, Romney also hinted that the state could soon fall in the GOP column, though it hasn't voted for a Republican presidential candidate since 1984.

"A blue state said we've seen a conservative governor, he cut back on the scale of government and has held down taxes and stood up to the public sector unions, and we want more of that not less of it. And I think you're going to find that in the decision that's being made in November," Romney said during a tele-town hall with small business owners.

Ryan, who returned to the state for a hometown hero's welcome Sunday night, has not made an endorsement in his state's Republican Senate battle.